Acoustic waves have been successfully utilized to perform both convolution and correlation of two signals in real time. For example, in U.S. Pat. No. 3,760,172 issued Sept. 18, 1973 to Calvin F. Quate, oppositely-propagating acoustic waves generated by the application of two signals to a piezoelectric medium are arranged to provide a second order parametric interaction adjacent an output electrode to provide the physical realization of convolution C.sub.n of two time functions f(t) and g(t) which is mathematically expressed as EQU C.sub.n = .intg.f(.tau.) g(t-.tau.) d.tau.
t being representative of the time displacement between the two functions. The time translation of the two functions is realized because of the opposite propagation directions of the two waves, the indicated multiplication is achieved by the nonlinear parametric interaction and the integration by the coupling of the product function to the output electrode. In the mentioned Quate U.S. Pat. No. 3,760,172, the process is achieved specifically with bulk acoustic waves, but surface acoustic waves can also be utilized as explained by Gordon S. Kino in U.S. patent application Ser. No. 190,342, and now U.S. Pat. 3,816,753. Furthermore, the nonlinearities obtained in the acoustic medium are relatively weak and various techniques have been subsequently developed to improve the efficiency of operation, such as utilization of the nonlinear properties of semiconductors as explained in the article "Signal Processing by Parametric Interactions in Delay-Line Devices" by Kino et al. in IEEE Transactions, Vol. MTT-21, No. 4, April 1973 (pp. 244-255).
Correlation, the time-reversed operation mathematically represented by EQU C.sub.r = .intg. f(.tau.) g(.tau.-t) d.tau.
Is particularly significant for utilization in so-called "correlation" radars and pattern recognition, but is not so simply achieved because of the time-reversal requirement. Typically, it requires a two-step operation, first a time reversal of a signal and then a convolution operation as briefly described, one specific example being described in detail in the above-mentioned Kino U.S. patent application Ser. No. 190,342.